1. Field of the Invention
The present invention relates to an electron-beam exposure system which corrects a proximity effect in electron-beam exposure.
2. Description of the Prior Art
In these years, electron-beam exposure systems have been increasingly used for forming fine patterns in a lithographic process in manufacturing semiconductor devices and the like.
With regard to electron-beam exposure systems, it is known that a phenomenon in which the line width and the like of a pattern transferred onto a resist is different from its design value stems from influence of what is termed as the proximity effect, in which incident electrons are scattered in the resist.
FIG. 1 is a diagram schematically showing the proximity effect stemming from forward scattering and back scattering of electron beams. In a case where rectangular patterns P1 and P2 which are parallel with each other as shown in FIG. 1A are intended to be exposed, if an electron-beam exposure is performed on the patterns P1 and P2 in accordance with a design pattern indicating a desired pattern, their post-exposure patterns take on patterns P1a and P2a, respectively, as shown in FIG. 1B. In other words, the widths of the patterns become larger than the design values in the middle portions respectively of the patterns which face each other. This is because the back scattering of the electron beam from every part of each pattern is greatly influential.
Against the background of such a proximity effect, consideration has been made for various methods of correcting the proximity effect for the purpose of obtaining patterns formed exactly on design values by predicting condition in which an electron-beam is scattered, and by thus changing the exposure.
FIG. 1C shows a method of correcting a proximity effect by changing the intensity of electron-beam irradiation. In a case where patterns are intended to be exposed, if the entire area of each pattern is exposed with a single intensity of electron-beam irradiation, this causes a proximity effect as shown in FIG. 1B. Taking this into consideration, the proximity effect is corrected by reducing the intensity of an electron-beam irradiated on parts (parts denoted by P3 and P4 in FIG. 1C) of the Pattern P1 and P2, the parts being proximate to other patterns.
With regard to a technique concerned with this, for example, Japanese Patent Official Gazette No. 3340387 has disclosed an electron-beam writing system capable of making a precise exposure map without making a shot size finer.
In addition, Japanese Patent Application Official Gazette No. 2003-218014 has disclosed a charged-particle-beam exposure system for making patterns which are highly precise in dimensions by exposing the patterns for extracting parameters in accordance with pattern data for extracting the parameters of a distribution function of exposure intensity on which a proximity-effect correcting process has been performed.
For the purpose of optimizing exposure respectively for patterns to be exposed so that the patterns to be exposed can obtain the same level of energy to be absorbed against the proximity effect, the proximity-effect correcting process for calculating the exposure for each pattern to be exposed on the basis of a distribution function of exposure intensity and a distribution function of accumulated energy, as described above. The distribution function of accumulated energy is expressed by use of the distribution function of exposure intensity and a convolution integral. For example, an equation expressing influence of back scattering by a Gaussian distribution function as shown in Equation (1) is used for the distribution function of accumulated energy.
                              2          ⁢                      E            ⁡                          (              x              )                                      =                              D            ⁡                          (              x              )                                +                                                    2                ⁢                η                            π                        ⁢                          ∫                                                exp                  ⁡                                      (                                          -                                                                                                    (                                                          x                              -                                                              x                                ′                                                                                      )                                                    2                                                                          β                          2                                                                                      )                                                  ⁢                                  D                  ⁡                                      (                                          x                      ′                                        )                                                  ⁢                                  p                  ⁡                                      (                                          x                      ′                                        )                                                  ⁢                                  ⅆ                                      x                    ′                                                                                                          Equation        ⁢                                  ⁢                  (          1          )                    where p denotes a density of patterns with respect to an area (average coverage factor in a mesh), D denotes a distribution of exposure imparted, E denotes an accumulated energy, and η denotes a coefficient indicating a ratio of back scattering. In addition, β denotes the length of the back scattering, and indicates an amount having a length dimension equivalent, for example, to approximately 8 μm. These parameters vary depending on a material of the substrate and an acceleration voltage of the electron beam.
In the light-hand side of Equation (1), the first and the second terms are referred to as a term expressing the forward scattering and a term expressing the back scattering, respectively. The forward scattering has a larger influence on a narrower range, and the back scattering has a smaller influence on a wider range. In this equation, the effect of the forward scattering is ignored, and it is assumed that the distribution of the imparted exposure is the distribution of energy contributing to sensitizing as it is. In the case where, for example, a voltage of accelerating the electron beam is approximately 50 kV, the length of the forward scattering is not larger than 0.05 μm. As a result, the effect of the forward scattering can be ignored when the calculation is performed for correcting the proximity effect.
If the equation (1) is solved to figure out D, this makes it possible to obtain an appropriate exposure. Such an equation includes a large number of divisions. Arithmetic has been heretofore performed on the equation by use of a CPU. This brings about a problem that the process rate is small. In addition, the correcting of the proximity effect by use of a CPU hinders the CPU from being used efficiently, and accordingly this affects the degree of utilization of the capacity of the exposure system.
Against this background, consideration has been made for increasing the processing rate by dividing a CPU into clusters. However, it takes time to transfer data among the clusters. For this reason, this clusterization has not offered an effective means for solving the problem yet.
Furthermore, a method of figuring out an appropriate exposure by performing a method of successive substitution on D is adopted while solving Equation (1). However, it is difficult to determine whether or not the solution is converged. For this reason, it has been a conventional practice that the calculation is performed to some extent, but that the calculation is terminated after that. As a result, there has been no guarantee that a precise value can be figured out.